Designing Common Source Amplifier with NMOS transistors

I am currently working on designing a Common Source amplifier with NMOS transistors. Unfortunately, I've had a few problems and don't seem to be making any progress. The requirements for the circuit are:

• Driving a load of 500 Ohms
• Maximum drain current of 100mA
• Maximum (W/L) of 1000
• Gain of 20dB (10V/V) at 10kHz
• Input is a 0.1V sine wave at 10kHz with a series resistance of 25kOhms
• Only source available is Vdd@5V (pictured) and GND

Furthermore, my given information is as follows: k = 10^-5 A/V^2, Vt (threshold voltage) = 1V, Lambda = 0.02

Now for what I've tried: Here, I've substituted many different values for R5 and R4, but my general approach is as follows.

1. Obtain the Q-Point values of Vgs and Id
2. Anaylze the circuit via small signal equivalent - doing so, I arrived at the equation Req = 1/((1/R6)+(1/R5)), where Av = (-𝓰ₘ)(Req), 𝓰ₘ being the transconductance value (which itself is equivalent to sqrt(2*k*Id_q)).
3. I calculated the input resistance as R2||R3 to obtain Rg = R2||R3 = 50kOhms.
4. For the output resistance, I disconnected the load and assumed the drain resistance to be arbitrarily large so that the output resistance, Ro = R5.

None of my solutions have yielded proper results and I was wondering what I'm doing wrong (any help is appreciated). Thanks.

• Step 2 should be step 1, the gain Av isn't determined only by the parallel value of R5 and R6 but also by R4. Determine a formula for Av with gm, R5, R6 and R4 as inputs. Note how the ratio Req/R4 is important. Pick a reasonable value for R5 like 100 ohms and see what R4 needs to be and what gm you need. Then do step 2 (your step 1) and determine Ids and Vgs from gm. – Bimpelrekkie Aug 28 '18 at 6:09 